The theoretical description of (nonlinear) spectroscopy is conventionally based on a semiclassical approach, where the light fields are treated classically and only the sample system is treated fully quantum mechanically [1]}, [2]}. In most situations, this approximation is extremely well justified, owing to the weak nonlinearity of light-matter interactions in free space [3]}.
Nevertheless, recent years have seen the rapid rise of theoretical investigations, as well as first proof-of-concept experiments that challenge this convention, and investigate how quantum properties of light can be applied or exploited beneficially in spectroscopic applications [4]}, [5]}, [6]}, [7]}, [8]}. This includes the use of photon correlation measurements to analyse the light fields emitted by a sample [9]}, [10]}, [11]}, [12]}, [13]} in single-molecule spectroscopy [14]}, [15]}, [16]}, or to exploit coincidence measurements to detect particular spectral features in the sample [17]}, [18]}, [19]}, [20]}, as well as the generation of photonic entanglement in fluorescent proteins [21]}.
